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This paper is dedicated to the study of the incompressible inviscid Boussinesq equations in the whole space \(\mathbb {R}^n\) ( \(n\geq 2\) ). We obtain the local well-posedness and blow-up criterion in a new framework, namely Besov-Herz spaces \(BK_{p,q,r}^{\alpha ,s}(\mathbb {R}^n)\) , covering critical and supercritical cases of regularity ( \(s\geq n/p+1\) ). To obtain such results, we need to obtain appropriate linear estimates for a linearized inviscid Boussinesq system in our setting.

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On the Well-posedness for the Inviscid Boussinesq Equations in Besov-Herz Spaces

  • 会议论文

  • 发表日期：

    2025年

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  • Daniel Ferreira Machado

摘要

This paper is dedicated to the study of the incompressible inviscid Boussinesq equations in the whole space \(\mathbb {R}^n\) ( \(n\geq 2\) ). We obtain the local well-posedness and blow-up criterion in a new framework, namely Besov-Herz spaces \(BK_{p,q,r}^{\alpha ,s}(\mathbb {R}^n)\) , covering critical and supercritical cases of regularity ( \(s\geq n/p+1\) ). To obtain such results, we need to obtain appropriate linear estimates for a linearized inviscid Boussinesq system in our setting.